RMC - Vol. 21 Num. 2 - Maryia Kabanava

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$%M. Kabanava, Tempered Radon measures, Rev. Mat. Complut. 21 (2008), no. 2, 553–564.%$

Tempered Radon Measures

Maryia KABANAVA

Mathematical Institute

Friedrich Schiller University Jena

D-07737 Jena, Germany

Received: December 11, 2007
Accepted: January 1, 2008

ABSTRACT

A tempered Radon measure is a $σ$ -finite Radon measure in $n ℝ$ which generates a tempered distribution. We prove the following assertions. A Radon measure $μ$ is tempered if, and only if, there is a real number $β$ such that $2β2 (1+ |x| ) μ$ is finite. A Radon measure is finite if, and only if, it belongs to the positive cone $+ B01∞ (ℝn )$ of $B01∞(ℝn)$ . Then $μ(ℝn)~ ∥μ|B01∞ (ℝn )∥$ (equivalent norms).

Key words: Radon measure, tempered distributions, Besov spaces.
2000 Mathematics Subject Classification: 42B35, 28C05.